Yes, fast HDD can always help but the real cause is the lack of polishing and the way the loading are integrated in the gameplay, you could say that those engine stalls are "programmed" by the devs and are inevitable.

And sometimes faster HDDs don't even help. For instance Thief have regular (and identical) framerate drops because of loading during gameplay both with HDD and with SSD, no difference at all.  

Some games, like for instance Trials fusion, are programmed to let the game run even if the assets are not fully loaded, you can then see incomplete textures (blurry textures) for a few moment in some areas. Others games forbid the lack of data and force the engine to completely freeze the game until the data is loaded into the system creating those mini pauses.

But normally by testing and polishing those problems are easily fixable.